The two largest auto manufacturers, Toyota and GM, have experimented with hydrogen powered cars in the past, and they are currently considering the decision to introduce a hydrogen powered car into the commercial automobile market. The payoffs from the possible actions are measured in millions of dollars per year, and the possible outcomes are summarized in the following game matrix: If both firms enter the market simultaneously, what is the Nash equilibrium?
A) Toyota produces and GM does not produce.
B) GM produces and Toyota does not produce.
C) There are two Nash equilibria-GM produces and Toyota does not produce, or Toyota produces and GM does not produce.
D) There is no Nash equilibrium in this game.

Question

The two largest auto manufacturers, Toyota and GM, have experimented with hydrogen powered cars in the past, and they are currently considering the decision to introduce a hydrogen powered car into the commercial automobile market. The payoffs from the possible actions are measured in millions of dollars per year, and the possible outcomes are summarized in the following game matrix:  If both firms enter the market simultaneously, what is the Nash equilibrium?
A) Toyota produces and GM does not produce. 
B) GM produces and Toyota does not produce. 
C) There are two Nash equilibria-GM produces and Toyota does not produce, or Toyota produces and GM does not produce. 
D) There is no Nash equilibrium in this game.

Quizplus · Accepted Answer

In this game, both firms have the option to produce or not produce a hydrogen-powered car. If one firm produces and the other does not, the firm that produces will have a payoff of $20 million, while the firm that does not produce will have a payoff of $0. If both firms produce, they will each have a payoff of $10 million.

To find the Nash equilibrium, we need to find the outcome where neither firm has an incentive to change their decision, given the decision of the other firm. In this case, if one firm produces, the other firm will always be better off not producing. This is because if the other firm produces as well, both firms will earn $10 million, which is less than the $20 million that one firm would earn if it was the only producer. Therefore, we can eliminate options A and B because they involve one firm producing while the other does not.

The only remaining option is C, which suggests that there are two Nash equilibria-GM produces and Toyota does not produce, or Toyota produces and GM does not produce. This is true because each firm is indifferent between producing and not producing if the other firm does not produce. Therefore, both outcomes are stable and there is no incentive for either firm to change their decision.

Overall, the best choice is C because it correctly identifies the two Nash equilibria in the game.

The Two Largest Auto Manufacturers, Toyota and GM, Have Experimented